The figure shows 2 tanks, Tank V and Tank W. Tank W is completely empty while Tank V is filled with water to the brim. Water from Tap U flows in at a rate of 1.2 litres per minute while water drains from Tap T at a rate of 2.16 litres per minute. Both taps are turned on at the same time. After some time, the heights of the water level in both tanks became the same.
- Find the time taken for the heights of the water level to be the same in both tanks.
- Find the height of the water level at that point of time.
(a)
Base area of Tank V
= 40 x 20
= 800 cm
2 1 ℓ = 1000 cm
3 1.2 ℓ = 1200 cm
3 2.16 ℓ = 2160 cm
3 Height increase per minute for Tank V
= 1200 ÷ 800
= 1.5 cm/min
Base area of Tank W
= 20 x 18
= 360 cm
2 Height decrease per minute for Tank W
= 2160 ÷ 360
= 6 cm/min
Let t be the time taken for both the water levels to become the same.
1.5 t = 12 - 6 t
7.5 t = 12
1 t = 1.6 min
(b)
Height of the water level
= 1.5 t
= 1.5 x 1.6
= 2.4 cm
Answer(s): (a) 1.6 min; (b) 2.4 cm